IDEAS home Printed from https://ideas.repec.org/a/spr/aistmt/v76y2024i2d10.1007_s10463-023-00889-z.html
   My bibliography  Save this article

Test for conditional quantile change in general conditional heteroscedastic time series models

Author

Listed:
  • Sangyeol Lee

    (Seoul National University)

  • Chang Kyeom Kim

    (Seoul National University)

Abstract

This study aims to test for detecting a change point in the conditional quantile of general location-scale time series models. This issue is quite important in risk management because the conditional quantile is utilized to measure the value-at-risk or expected shortfall of financial assets. In this paper, we design two types of cumulative sum tests based on the conditional quantiles. Their limiting null distributions are derived under regularity conditions, together with consistency of the proposed tests under the alternative. Monte Carlo simulations demonstrate the good performance of the proposed tests in terms of both stability and power for various time series settings. A real data analysis using the daily returns of the Brent Oil futures also confirms the validity of the tests in real-world applications.

Suggested Citation

  • Sangyeol Lee & Chang Kyeom Kim, 2024. "Test for conditional quantile change in general conditional heteroscedastic time series models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 76(2), pages 333-359, April.
    • Handle: RePEc:spr:aistmt:v:76:y:2024:i:2:d:10.1007_s10463-023-00889-z
    DOI: 10.1007/s10463-023-00889-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10463-023-00889-z
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10463-023-00889-z?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Meitz, Mika & Saikkonen, Pentti, 2008. "Ergodicity, Mixing, And Existence Of Moments Of A Class Of Markov Models With Applications To Garch And Acd Models," Econometric Theory, Cambridge University Press, vol. 24(5), pages 1291-1320, October.
    2. Kim, Minjo & Lee, Sangyeol, 2016. "Nonlinear expectile regression with application to Value-at-Risk and expected shortfall estimation," Computational Statistics & Data Analysis, Elsevier, vol. 94(C), pages 1-19.
    3. Xiao, Zhijie & Koenker, Roger, 2009. "Conditional Quantile Estimation for Generalized Autoregressive Conditional Heteroscedasticity Models," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1696-1712.
    4. Su, Liangjun & Xiao, Zhijie, 2008. "Testing for parameter stability in quantile regression models," Statistics & Probability Letters, Elsevier, vol. 78(16), pages 2768-2775, November.
    5. Gombay, Edit, 2008. "Change detection in autoregressive time series," Journal of Multivariate Analysis, Elsevier, vol. 99(3), pages 451-464, March.
    6. Qu, Zhongjun, 2008. "Testing for structural change in regression quantiles," Journal of Econometrics, Elsevier, vol. 146(1), pages 170-184, September.
    7. Sangyeol Lee & Jeongcheol Ha & Okyoung Na & Seongryong Na, 2003. "The Cusum Test for Parameter Change in Time Series Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(4), pages 781-796, December.
    8. Robert F. Engle & Simone Manganelli, 2004. "CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles," Journal of Business & Economic Statistics, American Statistical Association, vol. 22, pages 367-381, October.
    9. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    10. Sangyeol Lee & Jungsik Noh, 2013. "Quantile Regression Estimator for GARCH Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(1), pages 2-20, March.
    11. Jungsik Noh & Sangyeol Lee, 2016. "Quantile Regression for Location-Scale Time Series Models with Conditional Heteroscedasticity," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(3), pages 700-720, September.
    12. Zhou, Mi & Wang, Huixia Judy & Tang, Yanlin, 2015. "Sequential change point detection in linear quantile regression models," Statistics & Probability Letters, Elsevier, vol. 100(C), pages 98-103.
    13. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
    14. Paul H. Kupiec, 1995. "Techniques for verifying the accuracy of risk measurement models," Finance and Economics Discussion Series 95-24, Board of Governors of the Federal Reserve System (U.S.).
    15. Haejune Oh & Sangyeol Lee, 2018. "On score vector- and residual-based CUSUM tests in ARMA–GARCH models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(3), pages 385-406, August.
    16. Robert F. Engle & Simone Manganelli, 2004. "CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles," Journal of Business & Economic Statistics, American Statistical Association, vol. 22, pages 367-381, October.
    17. Haejune Oh & Sangyeol Lee, 2019. "Modified residual CUSUM test for location-scale time series models with heteroscedasticity," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(5), pages 1059-1091, October.
    18. Koenker, Roger & Zhao, Quanshui, 1996. "Conditional Quantile Estimation and Inference for Arch Models," Econometric Theory, Cambridge University Press, vol. 12(5), pages 793-813, December.
    19. de Pooter, M.D. & van Dijk, D.J.C., 2004. "Testing for changes in volatility in heteroskedastic time series - a further examination," Econometric Institute Research Papers EI 2004-38, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    20. Oka, Tatsushi & Qu, Zhongjun, 2011. "Estimating structural changes in regression quantiles," Journal of Econometrics, Elsevier, vol. 162(2), pages 248-267, June.
    21. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    22. Weiss, Andrew A., 1991. "Estimating Nonlinear Dynamic Models Using Least Absolute Error Estimation," Econometric Theory, Cambridge University Press, vol. 7(1), pages 46-68, March.
    23. Bougerol, Philippe & Picard, Nico, 1992. "Stationarity of Garch processes and of some nonnegative time series," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 115-127.
    24. Claudia Kirch & Joseph Tadjuidje Kamgaing, 2012. "Testing for parameter stability in nonlinear autoregressive models," Journal of Time Series Analysis, Wiley Blackwell, vol. 33(3), pages 365-385, May.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Vincenzo Candila & Giampiero M. Gallo & Lea Petrella, 2020. "Mixed--frequency quantile regressions to forecast Value--at--Risk and Expected Shortfall," Papers 2011.00552, arXiv.org, revised Mar 2023.
    2. Hubner, Stefan, 2016. "Topics in nonparametric identification and estimation," Other publications TiSEM 08fce56b-3193-46e0-871b-0, Tilburg University, School of Economics and Management.
    3. Donggyu Kim & Minseog Oh & Yazhen Wang, 2022. "Conditional quantile analysis for realized GARCH models," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(4), pages 640-665, July.
    4. Bruzda, Joanna, 2019. "Quantile smoothing in supply chain and logistics forecasting," International Journal of Production Economics, Elsevier, vol. 208(C), pages 122-139.
    5. Jungsik Noh & Sangyeol Lee, 2016. "Quantile Regression for Location-Scale Time Series Models with Conditional Heteroscedasticity," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(3), pages 700-720, September.
    6. Zhu, Qianqian & Zheng, Yao & Li, Guodong, 2018. "Linear double autoregression," Journal of Econometrics, Elsevier, vol. 207(1), pages 162-174.
    7. Catania, Leopoldo & Luati, Alessandra, 2023. "Semiparametric modeling of multiple quantiles," Journal of Econometrics, Elsevier, vol. 237(2).
    8. Komunjer, Ivana, 2013. "Quantile Prediction," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 961-994, Elsevier.
    9. Gareth W. Peters, 2018. "General Quantile Time Series Regressions for Applications in Population Demographics," Risks, MDPI, vol. 6(3), pages 1-47, September.
    10. Timo Dimitriadis & iaochun Liu & Julie Schnaitmann, 2023. "Encompassing Tests for Value at Risk and Expected Shortfall Multistep Forecasts Based on Inference on the Boundary," Journal of Financial Econometrics, Oxford University Press, vol. 21(2), pages 412-444.
    11. Wagner Piazza Gaglianone & Luiz Renato Lima & Oliver Linton & Daniel R. Smith, 2011. "Evaluating Value-at-Risk Models via Quantile Regression," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 29(1), pages 150-160, January.
    12. Wu, Qi & Yan, Xing, 2019. "Capturing deep tail risk via sequential learning of quantile dynamics," Journal of Economic Dynamics and Control, Elsevier, vol. 109(C).
    13. Tan, Shay-Kee & Ng, Kok-Haur & Chan, Jennifer So-Kuen & Mohamed, Ibrahim, 2019. "Quantile range-based volatility measure for modelling and forecasting volatility using high frequency data," The North American Journal of Economics and Finance, Elsevier, vol. 47(C), pages 537-551.
    14. Malin Song & Zixu Sui & Xin Zhao, 2023. "A risk measurement study evaluating the impact of COVID-19 on China's financial market using the QR-SGED-EGARCH model," Annals of Operations Research, Springer, vol. 330(1), pages 787-806, November.
    15. Wang, Meng & Chen, Zhao & Wang, Christina Dan, 2018. "Composite quantile regression for GARCH models using high-frequency data," Econometrics and Statistics, Elsevier, vol. 7(C), pages 115-133.
    16. Chen, Cathy W.S. & Gerlach, Richard & Hwang, Bruce B.K. & McAleer, Michael, 2012. "Forecasting Value-at-Risk using nonlinear regression quantiles and the intra-day range," International Journal of Forecasting, Elsevier, vol. 28(3), pages 557-574.
    17. Stéphane Goutte & David Guerreiro & Bilel Sanhaji & Sophie Saglio & Julien Chevallier, 2019. "International Financial Markets," Post-Print halshs-02183053, HAL.
    18. Hua, Jian & Manzan, Sebastiano, 2013. "Forecasting the return distribution using high-frequency volatility measures," Journal of Banking & Finance, Elsevier, vol. 37(11), pages 4381-4403.
    19. Zhang, Heng-Guo & Su, Chi-Wei & Song, Yan & Qiu, Shuqi & Xiao, Ran & Su, Fei, 2017. "Calculating Value-at-Risk for high-dimensional time series using a nonlinear random mapping model," Economic Modelling, Elsevier, vol. 67(C), pages 355-367.
    20. Rubia, Antonio & Sanchis-Marco, Lidia, 2013. "On downside risk predictability through liquidity and trading activity: A dynamic quantile approach," International Journal of Forecasting, Elsevier, vol. 29(1), pages 202-219.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:aistmt:v:76:y:2024:i:2:d:10.1007_s10463-023-00889-z. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.